I like the Raspberry Pi idea, I have given some thought to that as well.

Another alternative is a Linksys WRT54G series wifi router:
http://en.wikipedia.org/wiki/Linksys_WRT54G_series
They are a router, and they have a USB port and you can install your own Linux, so they can also function as a light-duty server. That way you only need space and power for one device instead of two.

Or, you can compromise and rent a virtual server, e.g.
http://www.linode.com/
$20/month; possibly cheaper and less hassle on an amortized basis. That way you control all the software, but not the hardware.